We developed methods to build confidence interval and bands to detect time-varying effects of treatments in Cox's proportional hazards regression model. Dr. Sundaram and her collaborators have addressed in the need for statistical inference which in confidence intervals and confidence bands which give more tighter intervals than the standard Wald-type (normal approximation based) confidence intervals/band. This work extended the results of Tian, Zucker and Wei (2005, JASA) and shows that the proposed intervals/bands are tighter than those proposed by Tian, Zucker and Wei. This was achieved by developing empirical likelihood (EL) point-wise confidence regions for the time-dependent regression coefficients via local partial likelihood smoothing. Asymptotic properties were established for the proposed methods. Extensive numerical studies conducted indicated that the EL point-wise/simultaneous confidence regions/bands have better performance than the Wald-type estimators. The proposed methods illustrated on two real examples: the gastric cancer data and the Mayo Clinic primary biliary cirrhosis data showed similar findings of more precise (narrower) confidence intervals (bands). [unreadable] [unreadable] [unreadable] Another project developed method for randomly truncated data which are frequently encountered when the study design is retrospective and/or due to inability of experimental design to be able to capture the study participant before the initiation of the event. For example, pregnant women get selected based on their first visit to the gynecologist for confirming their pregnancy, resulting in loss to follow up of women who had early pregnancy loss. Estimation based on randomly truncated data becomes very challenging as the risk set over time is non-monotonic, making it very different from random right censoring. One of the problems addressed by Dr. Sundaram is developing robust inference for two sample accelerated failure time data for this type of data. Dr. Sundaram has also developed robust methods for analyzing proportional odds model for randomly truncated data. Proportional odds model provides a useful alternative to proportional hazards when the hazards converge over time (e.g., for modeling treatments that are successful). The large sample properties like asymptotic normality and strong consistency of the proposed estimators were established and the finite sample properties investigated through extensive simulations indicating good performance. The proposed methods are easy to compute, which is not the case with likelihood based estimators as it is not possible to profile out the non-parametric (baseline odds function) as is done with proportional hazards and right censored data.